Modelling the respiratory system of intensive care patients can enable individualized mechanical ventilation therapy and reduce ventilator induced lung injuries. However, spontaneous breathing (SB) efforts result in asynchronous pressure waveforms that mask underlying respiratory mechanics. In this study, a nonlinear auto-regressive (NARX) model was identified using a modified Gauss-Newton (GN) approach, and demonstrated on data from one SB patient. The NARX model uses three pressure dependent basis functions to capture respiratory system elastance, and contains a single resistance coefficient and positive end expiratory pressure (PEEP) coefficient. The modified GN method exponentially reduces the contribution of large residuals on the step in the coefficients at each GN iteration. This approach allows the model to effectively ignore the anomaly in the pressure waveform due to SB efforts, while successfully describing the shape of normal breathing cycles. This method has the potential to be used in the ICU to more robustly capture patient-specific behaviour, and thus enable clinicians to select optimal ventilator settings and improve patient care